Surface Radiation Heat Transfer

In order to isolate the effect of the surface radiation heat transfer between reactor elements on (jg and tst. Cases 5 and 10 have been recomputed under adiabatie reactor conditions by suppressing both direct and reflective (siN = 8out = 0.0) radiation exchange with the inlet/outlet enclosures (allowing only for in-channel radiation exchange). Surface radiation of the channel walls was subsequently turned on or off by setting the channel surface emissivity either to its standard value (e = 0.6) or to zero (s = 0.0). Cases 15 and 16 in Table 8.2 pertain to a cordierite ehannel wall, while Cases 18 and 19 to a FeCr alloy one. Wall temperature profiles for Cases 15 and 16 at various time instanees during the startup phase are plotted in Fig. 8.14. 

For tig t fst, radiation becomes a major upstream heat transfer mechanism in the channel, enhancing the upstream propagation of the reaction front. A numerical experiment was conducted to quantify the effect of radiation on the apparent thermal conductivity of the solid wall, by recomputing Case 15 and assuming an artificial material (cordierite ) for the microreactor wall, which had essentially the same properties with cordierite in Table 8.1 except for a higher thermal conductivity the value of was increased at 0.5 W/mK steps, until fig and fit assumed values close to the ones of Case 16. For = 5.5 W/mK, ignition and steady-state times for a microreactor without surface radiation, became essentially identical to the characteristic times of a microreactor with — 2.0 W/mK and a surface emissivity of 8 = 0.6 (see Case 17 in Table 8.2). This apparent increase in the thermal conductivity of the solid, however, should not be confused with numerical models employing effective wall thermal conductivity for catalytic monoliths [23]. 

Finally, for microreactors with high wall thermal conductivity (Cases 18 and 19 of Table 8.2), simulations show that the wall temperatures become more spatially uniform and heat conduction in the wall dominates. This results in a weaker impact of radiation towards redistribution of energy within the channel for FeCr alloy microreactors (this is in contrast to the previously mentioned more pronounced effect of radiation on heat losses in the FeCr alloy). 

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In catalytic channels, the flat plate surface temperature in Eq. (3.32) is attained at the channel entry (x O). As the catalytic channel is not amenable to analytical solutions, simulations are provided next for the channel geometry shown in Fig. 3.3. A planar channel is considered in Fig. 3.3, with a length L = 75 mm, height 21) = 1.2 mm, and a wall thickness 5s = 50 pm. A 2D steady model for the gas and solid (described in Section 3.3) is used. The sohd thermal conductivity is k = 6W/m/K referring to FeCr alloy, a common material for catalytic honeycomb reactors in power generation (Carroni et al., 2003). Surface radiation heat transfer was accounted for, with an emissivity = 0.6 for each discretized catalytic surface element, while the inlet and outlet sections were treated as black bodies ( = 1.0). To illustrate differences between the surface temperatures of fuel-lean and fuel-rich hydrogen/air catalytic combustion, computed axial temperature profiles at the gas—wall interface y=h in Fig. 3.3) are shown in Fig. 3.4 for a lean (cp = 0.3) and a rich cp = 6.9) equivalence ratio, p = 1 bar, inlet temperature, and velocity Tj = 300 K and Uin = 10 m/s, respectively. The two selected equivalence ratios have the same adiabatic equilibrium temperature, T d=1189 K. 

In this chapter, a numerical investigation is undertaken to study the eoupled catalytic and gas-phase combustion processes in a methane-fueled microreaetor with catalytically aetive Pt walls. Simulations were carried out with the 2-D fiill elliptic model for both the gas and solid phases. Elementary hetero-Zhomogeneous chemical reaction schemes were included along with heat eonduction in the walls, surface radiation heat transfer, and external heat losses. The main objeetives were to investigate the interplay of hetero-Zhomogeneous combustion, transport, and heat transfer mechanisms in the microreactor and to delineate combustion stability maps in terms of the underlying parameters. 

This chapter is organized as follows. The numerical model is firstly presented, followed by an assessment of characteristic time scales which are relevant for the adopted quasisteady approach. The impact of pressure, solid material properties, equivalence ratio, inlet velocity, surface radiation heat transfer, and gas-phase chemistry on the transient microreactor response is then elaborated. Based on the outcome of the previous computations, implications for the design of microreactor systems are outlined. 

Surface radiation heat transfer played an important dual role for low thermal conductivity wall materials. On one side it increased hg by dissipating heat away from the initially formed hot spot zone. On the other side it reduced t t due to a more effective redistribution of energy inside the channel, by transferring heat from the hot rear to the colder front section. 

The novelty in the aforementioned studies is the use of a comprehensive numerical model for the investigation of catalytic microscale reactors which includes, for the first time in the literature, detailed heterogeneous and homogeneous chemical reaction mechanisms, two-dimensional treatment for both the gas and solid wall phases and surface radiation heat transfer, under both steady and transient (quasisteady) conditions. Moreover, a validated chemical kinetics model for the coupled catalytic and gas-phase combustion of propane (a fuel of particular interest for portable applications) is presented for the first time. 

In rotary devices, reradiation from the exposed shelf surface to the solids bed is a major design consideration. A treatise on furnaces, including radiative heat-transfer effects, is given by Ellwood and Danatos [Chem. Eng., 73(8), 174 (1966)]. For discussion of radiation heat-transfer computational methods, heat fliixes obtainable, and emissivity values, see Schornshort and Viskanta (ASME Paper 68-H 7-32), Sherman (ASME Paper 56-A-III), and the fohowing subsection. 

The net heat transfer between two surfaces according to Eq. (4.159) is proportional to the first or second power of the temperature difference hence the radiation heat transfer dominates at a high temperature or for large temperature differences. When the temperature difference is small, a heat transfer factor is used similar to that used for convective heat transfer ... 

Radiation heat transfer. The radiation heat transfer between two parallel planes is reduced by placing a parallel aluminum sheet in the middle of the gap. The surface temperatures are (9j = 40 °C and 62 = 5 °C, respectively the emissivities are ej = e, = 0.8.5. The emissivity of both sides of the aluminum... 

The radiation heat transfer (cf> ) from the heat loads such as machines, lamps, persons, and sun has to be determined separately for the lower zone ( ./ ) and upper zone (4>nn The radiation between zone wall surfaces ( 4 u uJ has to be determined as well. 

Equation 9.127 may be extended in order to determine the net rate of radiation heat transfer from a surface in an enclosure. If the enclosure contains n black surfaces, then the net heat transfer by radiation to surface i is given by ... 

Equations similar to equation 9.158 may be obtained for each of the surfaces in an enclosure, 1 = 1,1 = 2, 1 = 3, 1 = n and the resulting set of simultaneous equations may then be solved for the unknown radiosities, qoi,qm- qun The radiation heat transfer is then obtained from equation 9.140. This approach requires data on the areas and view factors for all pairs of surfaces in the enclosure and the emissivity, reflectivity and the black body emissive power for each surface. Should any surface be well insulated, then, in this case, Qj — 0 and ... 

From Karlsson and Quintiere [1], it can be shown that for an enclosure with blackbody surfaces (ew = 1), the radiation heat transfer rate out of the vent of area A0 is... 

It rather seems that 40 percent of the surface area of the radiator in Fig. 13.1 is submerged under water. If the water is drained out, does this mean that the rate of steam condensation will increase by the same 40 percent. Answer—yes Does this mean that the radiator heat transfer duty will increase by 40 percent Answer—not quite. 

K, i = radiation heat transfer coefficient from salt water surface to cover of still, B.t.u./hr., sq. ft., ° F. 

In Expression (3.96), grad-surf is the radiation heat transferred between S6 and any other visible surface of the electrode. Murthy and Fedorov [65] noted that the surface-to-surface approach (as in Equation 3.96) could lead to some temperature prediction mistakes. According to [65], more accurate results can be expected considering the absorption, emission or scattering in the media. On the present topic, there are still ongoing studies and a common position about the effect of considering the absorption, emission or scattering in the media is still a matter of clarification (see for example [79] and the apparently opposite position of [42] and [65]). 

Fig. 7.22 Internal surfaces involved in radiation heat transfer.

Radiation heat transfer accounts for the heat fluxes exchanged between the gas volume and the surrounding surfaces and the surrounding gas volumes ... 

The first three terms on the right hand side represent the radiation heat transfer between the gas volume and the fuel cell surfaces. Summation in j appearing in Equations (7. 10) and (7. 11) accounts for the contributions of the other surfaces constituting the fuel cavity. In the case of a cavity constituted of four fuel cells, the summation is constituted of the contributions due to surfaces. ..Z-1,Z,Z + 1,..., m — 1, m, m + 1,..., n — 1, n, n + 1. 

The zone method is an effective way to model radiation heat transfer when geometries are sufficiently simple as in this case (Hottel and Sarofim, 1967). The system is divided into subsystems, the zones, which can be either surfaces (in the case of solids) or volumes (in the case of non-transparent gases). In the case of the tubular SOFC, the zones are the internal and external surfaces of the cell slices, the external surface of the tube elements, the fuel elements. Each zone is considered as characterized by a unique temperature. A zone model is particularly suitable for to use in a model like the finite difference model introduced in Section 7.4.1. 

For two large parallel plates with grey surfaces, the heat transfer by radiation between them is given by putting Ai = A2 in equation 150 to give ... 

The processes of scattering and absorption of radiation in the atmosphere so significantly alter the spectral distribution that any similarity to extra terrestrial radiation is almost coincidental. Experiments with radiation between surfaces have shown that blackbody radiation theory can be extended successfully to many radiation heat transfer situations. In these situations the strict equilibrium requirements of the initial model have so far not proved to be necessary for practical designs. Most importantly the concept of temperature has proved useful in non-equilibrium radiation flux situations(3). 

The transport of thermal energy can be broken down into one or more of three mechanisms conduction--heat transfer via atomic vibrations in solids or kinetic interaction amongst atoms in gases1 convection - - heat rapidly removed from a surface by a mobile fluid or gas and radiation—heat transferred through a vacuum by electromagnetic waves. The discussion will begin with brief explanations of each. These concepts are important background in the optical measurement of temperature (optical pyrometry) and in experimental measurement of the thermally conductive behavior of materials. 

Thermal radiation can take place without a medium. Thermal radiation may be understood as being emitted by matter that is a consequence of the changes in the electronic configurations of its atoms or molecules. Solid surfaces, gases, and liquids all emit, absorb, and transmit thermal radiation to different extents. The radiation heat transfer phenomenon is described macroscopically by a modified form of the Stefan-Boltzmann law, which is... 

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